Does this have two removable discontinuities?

Question

f(x)= [(x-2)(x-1)] / [(x-2)(x-2)(x-1)]

Answer 1

Yes it has.
At each point x not equal 1 you can write this function as

(x-2)/(x-2)^2 so its limit if x=> 1 is -1 So giving f(1) value 1 the dis continuity is removed.
At all points x not 2
f(x) =1/(x-2) which as x=>2 tends to infinity

So there is only ONE removable discontinuity

Answer 2

There is a removable discontinuity at x = 1: for any x not equal to 1, f(x) = (x-2) / (x-2)^2, which is continuous at x = 1.

However, the discontinuity at x = 2 is not removable. For x not equal to 1 or 2, f(x) = 1 / (x-2) which goes to +∞ on one side and -∞ on the other.

So there is only one removable discontinuity.